Efficient computation of the Zassenhaus formula
نویسندگان
چکیده
A new recursive procedure to compute the Zassenhaus formula up to high order is presented, providing each exponent in the factorization directly as a linear combination of independent commutators and thus containing theminimumnumber of terms. The recursion can be easily implemented in a symbolic algebra package and requires much less computational effort, both in time and memory resources, than previous algorithms. In addition, by bounding appropriately each term in the recursion, it is possible to get a larger convergence domain of the Zassenhaus formula when it is formulated in a Banach algebra. © 2012 Elsevier B.V. All rights reserved.
منابع مشابه
Computing the Baker-Campbell-Hausdorff series and the Zassenhaus product
The Baker-Campbell-Hausdorff (BCH) series and the Zassenhaus product are of fundamental importance for the theory of Lie groups and their applications in physics. In this paper, various methods for the computation of the terms in these expansions are compared, and a new efficient approach for the calculation of the Zassenhaus terms is introduced. Mathematica implementations for the most efficie...
متن کاملA q-Analogue of the Zassenhaus Formula for Disentan- gling Exponential Operators
The general structure of a q-analogue of the Zassenhaus formula, the dual of the Baker-Campbell-Hausdorff formula for combining exponential operators, is derived and the first few terms of the disentanglement of a q-exponential operator are explicitly given.
متن کاملThe Factorization Algorithm of Berlekamp and Zassenhaus
We formalize the Berlekamp-Zassenhaus algorithm for factoring square-free integer polynomials in Isabelle/HOL. We further adapt an existing formalization of Yun’s square-free factorization algorithm to integer polynomials, and thus provide an efficient and certified factorization algorithm for arbitrary univariate polynomials. The algorithm first performs a factorization in the prime field GF(p...
متن کاملCALCULATION OF NON LIFTING POTENTIAL FLOW USING DESINGULARIZED CAUCHY\'S FORMULA
This paper discusses the disturbance velocity and potential as well as the total velocity formulation for non lifting potential flow problem. The problem is derived based on the Cauchy method formulation. The adding and subtracting back technique is used to desingularize the integral equations. The desingularized boundary integral equations are then discretized. The discretized equations can be...
متن کاملHigher order operator splitting methods via Zassenhaus product formula: Theory and applications
In this paper, we contribute higher order operator-splitting method improved by Zassenhaus product. We apply the contribution to classical and iterative splitting methods. The underlying analysis to obtain higher order operator-splitting methods is presented. While applying the methods to partial differential equations, the benefits of balancing time and spatial scales are discussed to accelera...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Computer Physics Communications
دوره 183 شماره
صفحات -
تاریخ انتشار 2012